Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle wvx = 111^{circ}$, what is $mangle uvx$?

Explanation:

Step1: Identify angle - relationship

$\angle WVX$ and $\angle UVX$ are supplementary angles (linear - pair of angles).

Step2: Use the supplementary - angle property

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle UVX = x$. Then $m\angle WVX+x = 180^{\circ}$. Given $m\angle WVX = 111^{\circ}$, we have $x=180^{\circ}-m\angle WVX$.

Step3: Calculate the angle measure

$x = 180 - 111=69^{\circ}$.

Answer:

$69$